In the capacitive method, which is based on the capacitance measurement of a capacitor, a complex dielectric constant of a thin film on a substrate can be measured by use of an LCR meter in the range of several GHz or lower (see “Patent Document 1” below, for example). The measurement limit on the high-frequency side is caused by a difficulty in correcting the effect of electrode loss and LC resonance caused by electrode inductance.
It is a general practice to use a resonator method in measuring a complex dielectric constant in the high frequency range. The complex dielectric constant of a thin film on a substrate can be determined by measuring a change in intensity and phase with respect to a propagating direction by use of a network analyzer on a strip line, micro-strip line, etc. constituted by its thin film and electrodes (see “Patent Document 2” below, for example). This method allows for measuring a complex dielectric constant in the range of 0.1 GHz-10 GHz. In this case, the measurement limit on the high-frequency side is determined by a fact that it is difficult to obtain the characteristic of the thin film only. That is, it is difficult to completely separate and remove the loss in the conductor configuring the line from the measurement.
In order to measure a complex dielectric constant of a thin film on a substrate in a higher frequency range, the cavity resonator method is used. Resonant frequency, Q value, etc. are measured by a network analyzer in the presence and in the absence of an on-substrate-film sample inserted in the cavity resonator to thereby determine a complex dielectric constant of the thin film (see “Patent Document 3” below, for example). With this method, measurement is feasible for a complex dielectric constant in the range of 1 GHz-50 GHz. The measurement limit on the high-frequency side, in this case, is determined by the physical size of the cavity resonator. Namely, the cavity resonator has dimensions that approximate the wavelength (approximately 6 mm at 50 GHz), in which case the dimensional accuracy of the cavity resonator is based on the fabrication accuracy in manufacturing the resonator. That is, if the dimensional accuracy is low, there are greater errors in measurement.
The capacitive and resonance methods are destructive measurements that require working on the measuring sample to be inserted, in order to match the dimensions to the measuring tool. However, this requires a considerable labor and cost. Meanwhile, where the exterior dimensions, particularly in a part contacting with the inner wall of the measuring tool, of a sample have low accuracy, significant errors of measurement occur thus making it difficult to implement a correct measurement.
There are two non-destructive measuring methods that do not require working on the sample to measure. One is a method to clamp a sample between waveguides, and the other is to irradiate a sample with light.
By clamping a sample between two waveguides, a network analyzer can measure a reflection coefficient at one aperture and a transmission coefficient at the other aperture. The absolute value and phase angle of these coefficients are substituted in a simultaneous equation deduced by resolving the Maxwell equation, thereby determining a complex dielectric constant of the thin film on the substrate (see “Patent Document 4” below, for example). This method, called a non-resonant technique, is of a non-destructive measurement. This method allows for measuring a complex dielectric constant in the range of 1 GHz-100 GHz (approximately 3 mm in wavelength). The measurement limit on the high-frequency side is determined by the fabrication accuracy of the waveguides, which is similar to the foregoing paragraphs [0004] and [0005].
For measuring a complex dielectric constant, there is an “optical measuring method” in the direction from higher frequency to lower frequency, which is separate from the “electric measuring method” in the direction from lower frequency to higher frequency. In the optical measurement technique, generally a complex dielectric constant-can be measured under atmospheric pressure without destruction of and contact with the sample. These optical measurement methods are called free space techniques.
In the method of determining a complex dielectric constant from an optical response (reflection or transmission light) when a sample is irradiated with light, the complex dielectric constant becomes difficult to measure as the ratio nd/λ becomes smaller provided that the sample has a thickness of d and a refractive index of n wherein a measuring wavelength is λ. This is because light is a wave that travels by repeating the wave “crest” and “root”. When the sample is thin, e.g. nd/λ=0.001 or around, the sample interacts with just a part between the “crest” and the “root” of the incident light so that it seems that a direct-current electric field is applied to the sample. That is, the capacitor on a direct current is a mere insulator wherein the complex dielectric constant approximates to a real constant. For the above reason, when the ratio nd/λ is small, there is a difficulty in measuring a complex dielectric constant.
When a complex dielectric constant of a thin film is determined by irradiating a transparent sample with light and measuring a transmission spectrum thereof, measurement becomes difficult as the thickness of the thin-film decreases and the measurement wavelength increases. The computation result of this situation is shown in FIG. 1. The results shown here are the computation results of transmittance spectra where the measurement wavelength is changed, and the sample thickness and complex dielectric constant fixed. A thickness and refractive index of the substrate (S) are 700 μm and 3.4155, respectively, while a thickness and refractive index of the thin film (F) are 0.4 μm and 1.812, respectively. In the figures, the solid line is a transmittance spectrum (T(F/S)) of a sample formed of a thin film on a substrate, while the dotted line is a transmittance spectrum (T(S)) of the substrate only. In the figures, the spectra are depicted for approximately two fringes.
In FIG. 1(a), the incident wavelength is about 5 μm (middle infrared ray) to have nd/λ=0.14; in FIGS. 1(b)-1(d), the wavelength is increased one order per each figure. In FIG. 1(d), the wavelength is about 5 mm (about 60 GHz in frequency), and nd/λ=0.00014. In FIGS. 1(c) and 1(d), there is substantially no difference between the transmittance spectrum (T(S)) through only the substrate and the transmittance spectrum (T(F/S)) through the thin film on the substrate, in which state there is quite a difficulty in determining a complex dielectric constant of the 0.4-μm thin film. Here, complex dielectric constant (∈) and complex refractive index (n) are held with a relationship of “a square of n equals ∈ (n2=∈)”. Refractive index, without “complex,” means a real part of the complex refractive index.
The free space method includes an approach to directly measure an amplitude and phase of a reflection coefficient at a fixed incident angle (see “Non-Patent Document 1” below, for example) and approaches to determine a complex dielectric constant from a dependence of reflectance upon incident angle, and a dependence of reflectance upon sample thickness and a dependence of reflectance upon frequency (see “Non-Patent Document 2” below, for example). In the measurement at a fixed incident angle, an expensive measuring apparatus such as a network analyzer is required to measure an amplitude and phase of the reflection coefficient. In the method in which the incident angle is changed, there is no need for a network analyzer because merely an energy reflectance is measured. However, it is common for both measurements to measure an absolute reflectance. This requires a metal plate equal in size to the sample as a reference sample. In a case where the metal plate is not provided in the same size and set-up position as the sample-to-measure, there arises a measurement error problem.
There is a new reflectance measurement method that does not require a metal reference sample. This is a method for determining a complex dielectric constant from a ratio of a TE-wave reflection coefficient to a TM-wave reflection coefficient of a sample irradiated with a circular-polarization electromagnetic wave in a millimeter-wave band (see “Patent Document 5” below, for example).
In the measurement using the free space method, sensitivity is generally low. As for the best data so far, complex dielectric constant is determined by irradiating a 925-GHz (λ=324 μm) sub-millimeter wave at a changing incident angle to a low-dielectric (Low-k) polymer thin film (n=1.7), which has a thickness d=3.27 μm on a silicon substrate and then measuring a reflectance at around a Brewster's angle (see “Non-Patent Document 3” below, for example). The value nd/λ in this case is 0.02.
As described above, in either an electric measurement or an optical measurement, it is generally difficult to measure a complex dielectric constant of a thin film on a substrate at a frequency in the range of 30 GHz-3 THz (100 μm-10 mm, in wavelength).
The frequency band, used today in communication systems, includes sub-microwave bands of 1.9 GHz and 2.45 GHz and a sub-millimeter band of 19 GHz. The sub-microwave band is assigned to the personal handy phone system (PHS) and the medium-speed wireless LAN internal radio device. Meanwhile, the sub-millimeter-wave band is assigned to the high-speed wireless LAN internal radio device.
Furthermore, development in the future is expected for the higher frequency range of 30 GHz-3 THz. Research and development is active for a codeless communication system in a 50 GHz band and a collision-prevention vehicular radar and ultra high-speed wireless LAN in 60 and 70 GHz bands. Thus, a drastic progress is expected for the information communication technology. Furthermore, in the higher frequency range, practical applications at present are made in the millimeter/sub-millimeter wave astronomy and nuclear-fusion plasma research and development. Thus, the higher frequency range plays an important role. In order to develop a new device for use in the higher frequency range, it is essential to measure a complex dielectric constant of the existing and novel substances in the higher frequency range, which is important technology.
Due to the increase in integration and miniaturization of the devices in the semiconductor industries, the quality of semiconductor wafers is strictly required. Particularly, high flatness is required for a semiconductor wafer used as a substrate. The requirement has been satisfied each time by the conspicuous advancement of polish technology.
However, in order to improve flatness, there is a need for, in addition to polish technology, an accurate method and device for measuring flatness in order to evaluate the semiconductor wafer. The capacitive method and the optical interference method are the methods that are broadly used in measuring a thickness of a product semiconductor. These methods are capable of non-contact evaluation of a flatness of the entire surface of a wafer.
In the capacitive method, a sample is inserted between two opposite electrodes (parallel-plate capacitor) to thereby detect a capacitance change and hence measure a sample local thickness. The sample surface is scanned by the capacitor to determine a flatness of the entire surface (see “Patent Document 6”, for example). The capacitive method is advantageous because it is affected less by particles compared to optical-interference-scheme flatness measurement. Furthermore, the capacitive method can measure a thickness and flatness of a wafer of the type ranging from a slice wafer to a wafer with a pattern in the non-contact manner. However, this method requires applying a surface active agent solution to a semiconductor wafer surface. Furthermore, pre-processing is required to remove a native oxide film existing in the semiconductor wafer surface.
In the interference method, a semiconductor wafer is irradiated with an infrared ray and the reflection light from the sample is converted into an electric signal by a photodetector. In the spectrum measured, there appear fringes resulting from multi-reflection within the semiconductor wafer. A local thickness of the sample is determined from the interval of the fringes. The light irradiation point is scanned over the sample surface, to determine a flatness over the entire surface (see “Patent Document 7” below, for example). This process does not require a pre-processing and in-situ measurement is available during a polish process.
Today, in practical application a flatness of 1-5 μm can be achieved by a polish process (see “Patent Document 7” below, for example). In a case where a substrate surface form before polishing is measured by a flat measurer, and the substrate is deformed while being vacuum-absorbed by a rectification chuck and rectified into a desired form on the basis of the measurement result so that the polish keeps the rectified form, then a flatness of 0.3 μm can be achieved (see “Patent Document 8” below, for example).
[Patent Document 1] JP-A-2002-286771
[Patent Document 2] JP-A-11-166952
[Patent Document 3] JP-A-2002-228600
[Patent Document 4] JP-A-2002-214161
[Patent Document 5] JP-A-2000-193608
[Patent Document 6] JP-A-10-281710
[Patent Document 7] JP-A-8-216016
[Patent Document 8] JP-A-5-315307
[Non-patent document 1] Functional Material, Vol. 18, No. 10, (1998), p. 47
[Non-patent document 2] The Institute of Electronics, Information and Communication Engineers, Paper, B-II, Vol. J80-BII, No 10, (1997), p. 906
[Non-patent Document 3] Applied Physics Letter vol. 74, (1999), 2113-2115
[Non-patent Document 4] Optics/Electro-optics II, Authors: Kunio Fujiwara, Sigeo Yamaguchi (Asakura Physics Course 12, Asakura Bookstore), p 138-156.